Mitigating Noise-Induced Gradient Vanishing in Variational Quantum Algorithm Training

TL;DR

This paper introduces a new training scheme for variational quantum algorithms that mitigates noise-induced gradient vanishing, enabling more effective training on noisy quantum hardware.

Contribution

It proposes a novel cost function and proof that it can replace the original, improving gradient signals and training effectiveness under realistic noise conditions.

Findings

Significantly enhances gradient magnitudes using traceless observables.

Proves equivalence of minima between new and original cost functions.

Demonstrates effectiveness across various variational quantum algorithms.

Abstract

Variational quantum algorithms are expected to demonstrate the advantage of quantum computing on near-term noisy quantum computers. However, training such variational quantum algorithms suffers from gradient vanishing as the size of the algorithm increases. Previous work cannot handle the gradient vanishing induced by the inevitable noise effects on realistic quantum hardware. In this paper, we propose a novel training scheme to mitigate such noise-induced gradient vanishing. We first introduce a new cost function of which the gradients are significantly augmented by employing traceless observables in truncated subspace. We then prove that the same minimum can be reached by optimizing the original cost function with the gradients from the new cost function. Experiments show that our new training scheme is highly effective for major variational quantum algorithms of various tasks.